Ambient occlusion where two meshes overlap?
For this model rather than using the World ambient occlusion why not instead bake an ambient occlusion map on the model itself? There are hundreds of resources available for how to go about accomplishing this however I would recommend using this website as a source.

http://www.katsbits.com/tutorials/blender/basic-ambient-occlusion.php

You can bake the ambient occlusion on both the box as well as the ground mesh giving you more control in how it looks.